In WO 2014/154435 A1, a brake system for a vehicle and a method for operating the brake system are described. The brake system has a master brake cylinder and two brake circuits connected to the master brake cylinder, wherein each of the two brake circuits is connected via a normally open valve to a pressure chamber of the master brake cylinder that is associated therewith. Moreover, the brake system comprises a piston-cylinder mechanism with a piston that is displaceable by means of a motor and that bounds an intermediate storage volume of the piston-cylinder mechanism. Each of the two brake circuits of the brake system is hydraulically connected to the intermediate storage volume via a normally closed valve.